How create an AI that continuously adapts to different users?
Assuming you have enough training data and representational capacity, you can give each user a unique identifier and concatenate that with the other inputs to the neural net. As users give more feedback, the network will learn in the usual way since each situation (e.g. food-user pair) is represented by a unique input.

I'd consider this a general, brute-force approach, and it may not be suited to your application. Others' links to recommendation systems might be more useful. It depends on what your task is and what your constraints are.